Jamaal Lascelles's towering 76th-minute header proved decisive as the visitors secured a victory to give absent manager Benitez a timely boost as he recovers from hernia surgery.
The Spaniard was believed to have scheduled for a helicopter to take him to and from the Liberty Stadium, but ultimately he was too unwell to attend.
Moreno told Sky Sports News after the game: "I feel very happy, very glad for the performance of the players and we were on the way. We have been working very hard during the week and now it is a good moment. Rafa has been quite active, speaking with one of the staff and that has worked. Everyone contributed and it was fine.
"We expected them to play with five at the back and we realised it was four but everything was as planned. We tried to control their midfielders and attack down wide. Jamaal Lascelles has the spirit of a captain, without doubt. He manages everything so well and involved in all situations.
"We need Rafa back as soon as possible. This week he will join us, probably on Tuesday."
The result marks Newcastle's first away win in the Premier League since December 2015 and sees the Magpies climb into the top half of the table.